All I know is that decent noise cancelling over-ear headphones (Bose QC35 in my case) are really good at cancelling exactly that sort of noise - the hum plus whoosh of a box fan. Given that they are ineffective for high frequencies but very effective for the low frequency part of the spectrum where most of the fan noise (or airplane roar, or bus engine) is, I also always assumed that they played the least-possible-delayed anti-wave to cancel out the wave. Doesn't work for speech, sadly, since that has enough high-frequency energy to be intelligible even through these phones.